Eigenvalues of a spatial weights matrix: for spatial regression with raster data

Approximate eigenvalues for the row-standardized spatial connectivity matrix W of a regular tessellation, e.g., remotely sensed imagery.

eigen_grid(row = 5, col = 5)

Source

Griffith, Daniel A. (2000). Eigenfunction properties and approximations of selected incidence matrices employed in spatial analyses. Linear Algebra and its Applications 321 (1-3): 95-112. doi:10.1016/S0024-3795(00)00031-8 .

Arguments

row: Number of rows in the raster dataset
col: Number of columns in the raster dataset

Value

Returns the eigenvalues of the row-standardized spatial weights matrix (a numeric vector length row * col).

Details

Uses Equation 5 from Griffith (2000) to calculate the eigenvalues for a row-standardized spatial weights matrix; this is valid for a regular tessellation (rectangular grid or raster). The rook criteria is used to define adjacency.

The purpose is to calculate eigenvalues of the spatial weights matrix for the CAR and SAR models, enabling spatial regression with large raster data sets. This function is used internally by prep_sar_data2 and prep_car_data2. For more details, see: vignette("raster-regression", package = "geostan").

Examples